Math Problem Statement

\lim_{x \to 0} \sqrt{x^2 + 1} - 1

Solution

The equation in the image appears to be:

limx0x2+11\lim_{x \to 0} \sqrt{x^2 + 1} - 1

Would you like me to evaluate this limit and explain the steps?

Also, here are 5 related questions to consider:

  1. What is the general approach to evaluating limits with square roots?
  2. Can limits involving square roots be simplified using rationalization?
  3. How can L'Hopital's rule be applied to limits?
  4. What are indeterminate forms in limits?
  5. What happens to the function x2+1\sqrt{x^2 + 1} as xx approaches infinity?

Tip: Rationalizing the expression involving square roots often helps simplify limits.

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Math Problem Analysis

Mathematical Concepts

Limits
Square Roots
Indeterminate Forms

Formulas

\lim_{x \to a} f(x)
Rationalization technique

Theorems

L'Hopital's Rule
Squeeze Theorem

Suitable Grade Level

Grades 11-12